Question

utility function is u(x,y) = 6x^.5+y , and his budget constraint is px*x +y = m,

m=30

px=2

py = 1.

a.What is his original highest utility

level?

Now px has decreased to 1, m and py do not change.

b.What is his new maximum utility level?

Answer 1

Solution:

a.). Utility function (U_X,Y) = 6x^0.5 + y

To maximize utility: $\frac{MU_{X} }{P_{X}} = \frac{MU_{Y} }{P_{Y}}$

MU_X = $\frac{\partial U} {\partial X}$ = 3x^-0.5

MU_Y = $\frac{\partial U} {\partial Y} = 1$

Price of x = 2

Price of y = 1

$\frac{3X^{-0.5} }{2} = \frac{1}{1}$

X = 2.25

Budget constraint: PxX + Y = M

2X + Y = 30

X = 2.25

2(2.25) + Y = 30

4.5 + Y = 30

Y = 25.5

Highest utility: U(x,y) = (2.5, 25.5)

 

b.). New budget constraint: PxX + Y = M

X + Y = 30

X = 2.25

2.25 + Y = 30

Y = 27.75

New maximum utility: U(x,y) = (2.5, 27.75)